{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# List of Basic Regressions"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Linear Regression"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import scipy.stats as stats\n",
        "from statsmodels import regression\n",
        "from statsmodels import regression, stats\n",
        "import scipy as sp\n",
        "import statsmodels.api as sm\n",
        "import math\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "import yfinance as yf\n",
        "yf.pdr_override()"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:09.885Z",
          "iopub.execute_input": "2022-04-14T00:27:09.890Z",
          "shell.execute_reply": "2022-04-14T00:27:10.503Z",
          "iopub.status.idle": "2022-04-14T00:27:10.454Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "start = '2018-01-01'\n",
        "end = '2022-01-01'\n",
        "market1 = 'SPY'\n",
        "market2 = '^IXIC'\n",
        "symbol1 = 'AMD'\n",
        "symbol2 = 'INTC'"
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:10.463Z",
          "iopub.execute_input": "2022-04-14T00:27:10.468Z",
          "iopub.status.idle": "2022-04-14T00:27:10.478Z",
          "shell.execute_reply": "2022-04-14T00:27:10.507Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "asset1 = yf.download(symbol1, start=start, end=end)['Adj Close']\n",
        "asset2 = yf.download(symbol2, start=start, end=end)['Adj Close']\n",
        "benchmark = yf.download(market1, start=start, end=end)['Adj Close']"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 completed\n",
            "[*********************100%***********************]  1 of 1 completed\n",
            "[*********************100%***********************]  1 of 1 completed\n"
          ]
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:10.487Z",
          "iopub.execute_input": "2022-04-14T00:27:10.494Z",
          "shell.execute_reply": "2022-04-14T00:27:11.947Z",
          "iopub.status.idle": "2022-04-14T00:27:11.954Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def linreg(X,Y):\n",
        "    # Running the linear regression\n",
        "    X = sm.add_constant(X)\n",
        "    model = regression.linear_model.OLS(Y, X).fit()\n",
        "    a = model.params[0]\n",
        "    b = model.params[1]\n",
        "    X = X[:, 1]\n",
        "\n",
        "    # Return summary of the regression and plot results\n",
        "    X2 = np.linspace(X.min(), X.max(), 100)\n",
        "    Y_hat = X2 * b + a\n",
        "    plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n",
        "    plt.plot(X2, Y_hat, 'r', alpha=0.9);  # Add the regression line, colored in red\n",
        "    plt.xlabel('X Value')\n",
        "    plt.ylabel('Y Value')\n",
        "    return model.summary()\n"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:11.964Z",
          "iopub.execute_input": "2022-04-14T00:27:11.969Z",
          "iopub.status.idle": "2022-04-14T00:27:11.979Z",
          "shell.execute_reply": "2022-04-14T00:27:12.015Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "r_a = asset1.pct_change()[1:].dropna()\n",
        "r_b = benchmark.pct_change()[1:].dropna()\n",
        "\n",
        "linreg(r_b.values, r_a.values)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:                      y   R-squared:                       0.298\nModel:                            OLS   Adj. R-squared:                  0.298\nMethod:                 Least Squares   F-statistic:                     427.4\nDate:                Wed, 13 Apr 2022   Prob (F-statistic):           2.13e-79\nTime:                        17:27:11   Log-Likelihood:                 2125.5\nNo. Observations:                1007   AIC:                            -4247.\nDf Residuals:                    1005   BIC:                            -4237.\nDf Model:                           1                                         \nCovariance Type:            nonrobust                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------\nconst          0.0021      0.001      2.282      0.023       0.000       0.004\nx1             1.4588      0.071     20.674      0.000       1.320       1.597\n==============================================================================\nOmnibus:                      219.316   Durbin-Watson:                   2.080\nProb(Omnibus):                  0.000   Jarque-Bera (JB):             1465.582\nSkew:                           0.820   Prob(JB):                         0.00\nKurtosis:                       8.678   Cond. No.                         76.3\n==============================================================================\n\nNotes:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n\"\"\"",
            "text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.298</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.298</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   427.4</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Wed, 13 Apr 2022</td> <th>  Prob (F-statistic):</th> <td>2.13e-79</td>\n</tr>\n<tr>\n  <th>Time:</th>                 <td>17:27:11</td>     <th>  Log-Likelihood:    </th> <td>  2125.5</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>  1007</td>      <th>  AIC:               </th> <td>  -4247.</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>  1005</td>      <th>  BIC:               </th> <td>  -4237.</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>const</th> <td>    0.0021</td> <td>    0.001</td> <td>    2.282</td> <td> 0.023</td> <td>    0.000</td> <td>    0.004</td>\n</tr>\n<tr>\n  <th>x1</th>    <td>    1.4588</td> <td>    0.071</td> <td>   20.674</td> <td> 0.000</td> <td>    1.320</td> <td>    1.597</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>219.316</td> <th>  Durbin-Watson:     </th> <td>   2.080</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1465.582</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.820</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 8.678</td>  <th>  Cond. No.          </th> <td>    76.3</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
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          "metadata": {
            "needs_background": "light"
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        }
      ],
      "execution_count": 5,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:11.987Z",
          "iopub.execute_input": "2022-04-14T00:27:11.993Z",
          "iopub.status.idle": "2022-04-14T00:27:12.083Z",
          "shell.execute_reply": "2022-04-14T00:27:12.107Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sns.regplot(r_b.values, r_a.values)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
          "data": {
            "text/plain": "<AxesSubplot:>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 6,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.092Z",
          "iopub.execute_input": "2022-04-14T00:27:12.097Z",
          "iopub.status.idle": "2022-04-14T00:27:12.292Z",
          "shell.execute_reply": "2022-04-14T00:27:12.284Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Regression Model Instability"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def linreg(X,Y):\n",
        "    x = sm.add_constant(X) # Add a row of 1's so that our model has a constant term\n",
        "    model = regression.linear_model.OLS(Y, x).fit()\n",
        "    return model.params[0], model.params[1] # Return the coefficients of the linear model"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.303Z",
          "iopub.execute_input": "2022-04-14T00:27:12.312Z",
          "iopub.status.idle": "2022-04-14T00:27:12.323Z",
          "shell.execute_reply": "2022-04-14T00:27:12.402Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "breakpoint = 100\n",
        "xs = np.arange(len(asset1))\n",
        "xs2 = np.arange(breakpoint)\n",
        "xs3 = np.arange(len(asset1) - breakpoint)"
      ],
      "outputs": [],
      "execution_count": 8,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.334Z",
          "iopub.execute_input": "2022-04-14T00:27:12.341Z",
          "iopub.status.idle": "2022-04-14T00:27:12.352Z",
          "shell.execute_reply": "2022-04-14T00:27:12.407Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a, b = linreg(xs, asset1)\n",
        "a2, b2 = linreg(xs2, asset1[:breakpoint])\n",
        "a3, b3 = linreg(xs3, asset1[breakpoint:])\n",
        "\n",
        "Y_hat = pd.Series(xs * b + a, index=asset1.index)\n",
        "Y_hat2 = pd.Series(xs2 * b2 + a2, index=asset1.index[:breakpoint])\n",
        "Y_hat3 = pd.Series(xs3 * b3 + a3, index=asset1.index[breakpoint:])"
      ],
      "outputs": [],
      "execution_count": 9,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.362Z",
          "iopub.execute_input": "2022-04-14T00:27:12.367Z",
          "iopub.status.idle": "2022-04-14T00:27:12.378Z",
          "shell.execute_reply": "2022-04-14T00:27:12.411Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "asset1.plot()\n",
        "Y_hat.plot(color='y')\n",
        "Y_hat2.plot(color='r')\n",
        "Y_hat3.plot(color='g')\n",
        "plt.title(symbol1 + ' Price')\n",
        "plt.ylabel('Price')"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": "Text(0, 0.5, 'Price')"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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zWY++FO/5gMzs5/CSClbuPpZfdk0gxz6apMggZl0xxM3v4sCaNCmIyCzgdCDbGNPHuSwS+ABIBnYA5xtj8sRqrzUNmACUAFcYY5Y1ZXxKKdVQReV2HBTxw65Z/GPeTHYV7CIhtDN3DHuak6Mz2Jv7Gjs2puPtHUGBnM+jv40hp7S6h3MZI7tF4+/j5c63cFBN3dbpDeDU/ZbdDcw1xnQD5jqfA5wGdHP+TAFeauLYlFKqQdIL03n6r/+S6n8lM1Y9QOfwzrw58b98f+oQBtrvJCfjGYKCetO37zccd1wq8UnP1UgIlriwADdFf3ia9E7BGPO7iCTvt/hMYIzz8WzgV+Au5/I3jTV7xUIRCReROGNMRlPGqJRSh7IhZwOP/fEYH639iIqqCgLNQJ4eM5pBQb9QXPQfcksCSEy8jbi4qwkK6uXab1inAKZPHsii7bm8vXAXAI6jnKCnqbmjTiG2xoU+E6juppcApNTYLtW5rFZSEJEpWHcSJCUd/ljkSinVEFWOKmavnM3bq97mlx2/4Oflx+X9zmdEqBBZ+QlBLAH60bXrdOLirsbLK7DOa4gIk/rHM6pbFOn5ZdgdhskNmEPBHdxa0WyMMSLSoLRpjJkBzAAYPHiwZ6dcpVSLk1OSw1sr32Lq/KlkF2fTo10P7hl+JeMiUvEufQ+HMazMG8SYQffRv8vph9XjODzQ16Mrl2tyR1LIqi4WEpE4INu5PA3oUGO7ROcypVQrU+UwrM/YS+/40FqDu23bXURJRRV9EsKaPaasoiwen/84r694nfyyfEZ2GM5Dg0+gv99yystfx6s8jPjEf7C24Byem5PDpLGjm30IiubgjqTwJXA5MNX5+4say28WkfeBYUCB1ico1Tr9uC6T699extUjOnH/6fvK4E98+jcAdkyd2CxxOIyDrzZ+xftr3+fjdR8jCOM7DePy5ADaVf6IIAQFTaBTpweJjj4PL68glizeBeTg58EtiI5GUzdJfQ+rUjlKRFKBB7CSwYcicjWwEzjfufm3WM1Rt2A1Sb2yKWNTSrlPZkEZAD+tz3Ilhfomrmkq5fZy3lltTWazJnsNwb7BXNFrDKdEbCXa9gfeRBKX9C/i4qYQGNh1v32tqTj9vVvfXQI0feujyQdYNa6ebQ1wU1PGo5Ryvwq7g7wSqwNYWl4pFXYHvt42Lp35l2ubcnsVS3bksXjHHm4/qXujHTu3JJeZy2fy5J9PklOSw4CYHjx87EBOCNmEmJ8ICupHfPxLxMVdic3mx1sLd7Ipcw3Xje5MYoRVkVxWaSUvvVNQSqmjYIyh0z21p4+0Owxr0wsYmBSBt9e+uoXCMjsXv2YlidtP6o4xhke+Wc8Z/eMZ0CG8wcdOL0znsXmP8fbqt8kvy2d4+67c1yuYvoEb8fWJJDr6Ytq3v5zQ0OGueoLdheXc//kaAIL9vbnrVGuMovJK607BT+8UlFLqyFXPN1Ctb0IYq9MKeG/RLrrGBLNw2x7Xunmbd7seG2NIyy9l5h/bmfnH9gbVNyxJX8Lzi57nrZVvYRMbEzp24+zoSjoFbiEoqA+JibOIjj4Xb+/Quvvu2BdP9dAWYBUfedkEHy9NCkqpNmZjZiHjn/udL246gf5H8A29pj+35tR6fmLPGFanFfDhklQ+XJJaa91P67Jdj+0Ow/uL9nVhKiyrJMS/7jSX+7a38+uOX3li/hP8uO1H/L18ubhrMuMjtpMYuIHo6AuIj7+OiIixB43Xu8ZFv8Q5/ebPG7L43y9bDv1mWzBNCkqpA/pxXSYA367OOOqkkLW3rNbzfolhTB6axHuLdtXZtmYCKausqnUhnr8ll1P7tK+zT35ZPtP/ms5LS14isyiT9oFhXN0lgnPa5xEeWE5s7J0kJt6On1/cYcVbUrFvys1Pl6dx9qAEfqyRrForTQpKqQOqrLL6h9Ys7z9SmQVl9I4PZW36XgBGdY9mdPdoEsL9eeqHTbW2ra6IBsiv8RhgwdacWklhW942nl3wLG+sfIPiimKGREdxXUc/hkUUEB02gMTE6URHn1Nvj+OD2b811NWzlzCsUyQA/6nRjLa10aSglDqgglLrguxtO/ry88y95cSH+TOhbxwfLUlxlcnfNLYr14zsTGpeCVUOGP/c77X2m/rdBgBevHgQN76zjNkLdvLgpN4szVjKtL+m8c6qdxCB0+LDODPWcExEJdHRVxAXdxWhoUOPON6icutO4dxBiXyyLJUKu4PVaQWM6xnDVSM6HfHrejpNCkqpA6ruT1BZ5WiE1yplUFI4N43tyk1j97X9FxH8fbzoGhNS737frLb6sHaPDXZNZnPCzKksSPuDYB9fzk20cW5CFd1jehIffwMxMRdgs/kddbz5JZV42YQnz+vHOYMSuPi1v8gvqSQm9Ohf25NpUlBKAVbZfUWVg9AalbjpBaXAgZNCaUUVDmMI8jv4paSgpJK8kkrah/ofMo4HzuhFVLAf8eEBnPvSnwA4KOL11U9QFf0u2UXbsO/24epk4ZxEB8lx55OQcBOhocfXGjLjaOUWVxAR6IPNJiRG7BvuOjpYkwIi0h1rfoNYY0wfEekHTDLGPNKk0Smlms2k//3BpqwiV5PPd//axarUAsDqcLY/h8NwzH/mALD9sQm1LshllVWk7CmhW6z17f9dZ2Xy8V2jDhnHlSdYRTO7C8uplBQKvb+h3O97Hvujkv7hvlzaA/qHBJNdeS7jRjyKn1/0Ubzr+qXmlfDeol0MddYh1JwDoWts/Xc0rcXhFhS+CtwDVAIYY1YBFzZVUEqp5rcpqwiw+gUA3PvZate6iqq6AxJ/vXrf0GRTv9vg2g/goa/WcvKzv5NTVM49n67m8TlWvcCxHSMOGUdlVSW/7viVm+ZcSrr/jRR5f8246EpmHOvN7LGnsjnjbu6fP5NnFp5Fif3wBs575betvPTr1sPaFuDOj1cBcEb/eAB8vW0khAfQPtSfU3vXbfnUmhxu8VGgMWbRfrdm9gNtrJRqWQpqtPDJK6kkIrB2P4D97xSMMdz63nLX81d+38alx3V0DQWxztnCaI2zcxrA4EMkhKKKImYtn8VT86eSUphBmI+N8xIMl3SKon+X22jf/nL8/Tuw5N1vXPvkl1YSEeR70Nd1OAyPOSurrxnZ6ZCdzi5+bSF/bs0FYPKQfQM3f3f7SAJ8vFptp7Vqh5sUckSkC2AAROQ89pv8RinVcpVW7mt+uSIlj63ZxbXW71+nUHP7at+uzmDKqC4AdIgMZGVqAf/7eV//go+uP67OPlWOKuanzGfWslf5cuMX5JUX0j0Y7j8GTk4eTrek64mNvQiRfeMMndq7PXPWWv0n8ksqgKA6r7s2vYClO/MY0z2Gcvu+WH/ftJtxx8TW2b6m+VushJDcLrBWB7bQg3SYa00ONynchDWxTU8RSQO2A5c0WVRKqWZV807gqjeWuB53jw3GmH2DwFWrbqpa07t/7aJPQhgxIX6uJLJkpzW0RZCvV606h3J7OTOXv8a0BU+yKW8nvjYYHQXndIzmlJ5TSEi4GT+/+otpokL23Rnkl1by59Yc/vnhSt64aijdneX9V76+mOzCcmAtATUGrkvNK633NYvL7QT6elHl2FcElhxVN9m0BYeVFIwx24CTRCQIsBljCps2LKVUc6o4QOuib28dyS3vLee7NZkk3/2NqxK6ungIYM1D4/l6ZTp3f7qai179i/6JYexfA1E961hWURavLXuZJ+c/TkFFKT1D4N5egZzedTzdk64mPPxEvLwOPrH9NSM689GSVMrtDrIKyrj7U6vuY/GOPXSPDWHr7iJnQrDUvKvJKSqv83p5xRUMfPhHgFrFZv+d1OegcbRWh1U4JiKPiki4MabYGFMoIhEioi2PlGol6mtdNLZHNN5eNkZ029diyOH8Jr1tt1W8NOuKwQT7eXPesYmubTIKythd46L874k9qfRez0UfnUGn5xK575cH6RZUyvQhnfl58ps8dHYWxw38lHbtJh4yIYD1DX7BPdbo+2/8ucO1fP6WHIrK7Zzx/B/17pcQHuCKu6a5G/YNXVHdk/q+iceQ1K5hPaBbi8MtPjrNGHNv9RNjTJ6ITADua5qwlFLNaf87hV//OYaoEKs9/tDkSNfyvWWVhAf6klNcjq+3jbE9YoDag8fZRCgut2NwYPf5gZdW38zyn3cQ5AUnxsD1/ScxsuedhIWdcMTxhvpbl660GsVB367OJDrYj5KKKu4/vRcPf72u1j59EkJZl7G31rI9xRXc8+mqOq8fFtA26g/qc7hJwUtE/Iwx5QAiEgC07h4cSrUhe/erI6hZnt4lOtj1+NhHfmLxv09i2c48OkYG1qoniA/zJ72gjD2lBVT5fsrekM/It5fgKIR7+yZzyYAb6Jxw2QHrChqiOgkVltduBLktx7oTiAqu2yKpd3wY36/N4pLX/uKtq4ciImzI2EtlleGliwfRNSaY7MJygv286RVfdyjttuJwk8I7wFwRed35/EpgdtOEpJRqTrlF5Vw2a9EB19tsQv/EMFamFlDlMAxylr/fO6Fnre1euqwz//jyRhbm/khJVRW9goTTgnrw4gUzCQtr3N7GBzJvszW6amSQLz3bh7Ahs5BpFw4gPjwAmwjP/LiJP7bkkLKnlMe/38A3qzLwsgn9OoSTEB7g6mzXlh1uRfPjIrKKfdNoPmyM+f5IDigiPYAPaizqDPwHCAeuBapn17jXGFN7mialVKNLy6+/RU5N/zmjt2vIiWpDnMVKG3ev4KGfrueLrYsorTL0D/Omi/dJJEf9i3G9+xIefnhDVR+ND6YM54IZC13PIwJ9mXP7qDrbjewWxbzNOdz3xRp+32Rdai4c0oGE8EPXZbQVhz32kTHmO+C7oz2gMWYjMABArMbHacBnWHcfzxpjnjraYyilDl91i5x3rxlGaWWVa2jrmtrV00Fsc85H3Df3Sb7dtQUvgdM7xHB87NXMmDeUJcaHs4f04LS+TZcQnr2gP3//YCVDkiMY1rkdHdsFsjO3BDhwn4JZVwyh27+/cyWEhPAAHjijd5PF2BIdNCmIyB/GmBEiUgi1WpkJYIwxR1vwNg7YaozZ2Ry3lkqpuoqds4pFh/jRLTak3s5dyVFBfHz9cVzwyi/EhH/CbtsXXPBVCUFecHXPPtx+/MP06XAWDofhxd+tG/zYkEMPfnc0Ojh7T+cWVwDw4XXH8eHiFPJKKmsNYFeTj5cNX2+bq7XVtSM74dtK51o+UgdNCsaYEc7fTVXQdiHwXo3nN4vIZcAS4A5jTN7+O4jIFGAKQFJSUhOFpVTbUd3R7GDDN+QXbeGHTXdQFfktC0vsRPnauHPQSdxz4uuEB+1rjmqzCbef1I3nftpMt9jgA75eY+gQaSWFPc6kEBvqzy3juh1yvztO7u4a9iJei43qOGTxkbOIZ60xpuehtm0IEfEFJmENtAfWKKwPY92RPAw8DVy1/37GmBlYvasZPHhw3VG6lFINYncOduez3zdmYxzM2/gs0xY+w9cp6VQ4oFNwAK+cfCsXH3s/QX7h9b7e7Sd154YxXfDz9qp3fWOJDvbj2I4R3DC6S4P2szv7WiS3C2Rsz5imCK1FO2RSMMZUichGEUkyxtSdTPXInQYsM8ZkOY+TVb1CRF4Fvm7EYymlDqDCdadgFeGWl2fy3eqHmbb4DX7NLsFL4Pxug7lkwE2c1vPyw2pF1NQJAay7kk9uOL7B+00emsSynXlMPbdfqx/c7kgcbkVzBLBWRBYBri6BxphJR3HsydQoOhKROGNM9SB7ZwNrjuK1lVKHqbr4qLx0BS8tup/pK+eyodAQ4evDzQPO4L5xM4gNbj3DRUcG+TLTOeyGqutwk8L9jXlQ5xhKJwPX1Vj8hIgMwCo+2rHfOqVUE3A4yvGq+JwRXacyanY2O0ogNiCQqWNu4sbh9xPip+3225pDtT7yB64HugKrgZnGmKOeR8EYUwy022/ZpUf7ukqpw1NRkc2KLY8zc/lM3t9RwF479I5M4K2TH+T8vpfh63XwOQpU63WoO4XZWLOtzcOqA+gF3NbUQSmlGp/DYSc39ytW7XyTF1Z8zpxMKK2CaK8uxJRfzKqbHsBm0zL2tu5QSaGXMaYvgIjMBA7cF14p5ZHKy9NIS3+Dt5c9zicphawuAB+bF2d0O5khUf/gpZ+sJp2aEBQcOim4Rskyxti1g5lSLYMxhsLCpWzZ8Thvr/2CT1Ir2VUCcUGRPDD6Fi7rfzmdIjrx5oIdwFpuGtuwZp2q9TpUUugvItV93gUIcD5vrB7NSqlGVFVVTHb2B6za9jwfbVnBB6lQZIehcQN4/LS7OL/3+dhk3x1BpbOPwpSRmhSU5VA9mpu+sbFS6qgVFMwnNe0V/tj6Ll9nVPFztlBSBSd3GsudI+5lXKdx9fYvsDubo3p7aSmAshz2gHhKKc9SVVVCTs5n7EqZzudbF/FZmrC+0OBr8+GCPhdy78h76Rl18IEIqnv3alJQ1TQpKNXClJdnkJb2AltSXuLb1D18mOZDRil0Dk/mxQn/4txe5xITdHjDN7jGPdJKZuWkSUGpFsDhKCcvby4ZGTPZmvEFn6Q6+CLDi72VcHziYJ4ddhvn9z6/wRPZfLvaGkTAZtM7BWXRpKCUBysrSyU9/SUyMmaxPi+TL9K9mZstlDuEkzuP475R93FChxOOeFazTVlFjRyxauk0KSjlgfLz51nJIOs9fs6GL7PCWZMH3ja4csCV3D78dnpF93J3mKoV0qSglBvNWZNJ5+gguseGYLcXsnv3J6SkPEVWwVp+zgng3ZQgskuLOSYqjmmnPsR5vc4jPiTe3WGrVkyTglJudP3bS4nwy+GjS1eRlfU2OSXZfJwRybcZwewpK2J44nBeOO4OzjnmnFr9CxpLoK8XJ+qcAqoGTQpKuYHDUUFK2uvccewM+kYvY95GL77JSeTLXd44TAETuk3gvlH3MSR+SK36gg+XpJC9t4xrR3U+5JwFz/y4ifcX7WLRv0+qtXzR9j18vDSFW07sRklFFWn5pU3yHlXLpElBqWZUUrKZzMzXSUt7kfLKArLsEUz/K4EtZWl4SSpTjp3CjUNupE9Mn7r7Vti58+NVADz1wyYuHNKBqef2o6jcjrdN+OdHKzm5VyxnDkgAYPrczYA15EXNxHLtm0soKK2kXbAfACfVMyezars0KSjVxOz2IvLzfyYjYxa5uV9TZK/it719eXHdDkqq8vDGcNcJd3HHcXcQHRR9wNfZkVNS6/n7i1N47Jy+9Hnge6KC/cgpKufrVRmupFCt3DlJvZ+3DRGhXZAvBaWVvPTrVgBuHKNDXKh9NCko1UTKy9NITX2OjIzXsdtzKXRE8fnuAXyxcxu5pavxq+pJlP0sYv2GM/WkMw/5en9uzamzLKOgDICconLXsuW78uifGO563vP+OQA8dk5fJg9NoltsMNtyrAkUR3aLOuLmrKp10qSgVCOqrMwjJ+cLsrPfIy/vJ8DG6oqBzN3dm6+2/oExuZzX6zzibOfzxeIATukVyy8bsw/rtYvLq+osm7Mms86ys1/8s979f1ibyRn94/l+rWs6dGbptJRqP27r2y4iO0RktYisEJElzmWRIvKjiGx2/o5wV3xKHS5jDHl5v7J27YXMnx/Nxo1XsqdwPUvtp3Pd6iRuXbCYBRkbuHnIzay9cS0f/u1Dios60rFdIIOTI6isMhSUVh7yOCUVdvy8a//L/vfrda7Hn954PIM71v2Xeeb8/ozpEc1vm3bT54HvXctfuGiQTlyv6nD3ncJYY0zNe+K7gbnGmKkicrfz+V3uCU2pg6uqKiE7+wPS0l6gqGgpSAAZvucxN8vOZ5t/YU/pl/SN6csrE2fgKBrN0l17OSb6GMDqSdwrLpSkyEAAduWW0Dcx7KDHKyq3E+znzXe3HUe53cFp0+bVWp8YEcCIblEs2ZnHgA7hjO0RQ4/2wYzv3Z4t2UX8unE3ABP7xfHo2X0JC/Bpgk9FtXTuTgr7OxMY43w8G/gVTQrKgxhj2Lt3IWlp/yMn5wscjmL8AvqyzHExb21azYqsDwjwDmBSj0lcM+gaxiaPZcqby5i7wWoJNO2nzUwe1oFde0q4dHhHkiKDANi5p5ikdoEE+XrhfYBv7/kllQT5edM5Opiyyn1FSd/fPoou0UF4e9m4fnQXAny8uPKETvjWuKvok7Av4Tx/4UAd60gdkDuTggF+EBEDvGKMmQHEGmMynOszAW0rpzxC9V1BauozFBevwds7Ep+ws/hhdyCvL/iBnQXv0CWiC6+f+TrnHnMu/t5BeIkgAot27HG9zrM/beL5n60EcWxyBEntrDuFnbkl3PzuD5w9MIFnLxhQ9/gOw59bcxjd3Wqd5O+zr49Cj/Yhrsf+Pl5cN7pua6KOzuME+nppQlAH5c6kMMIYkyYiMcCPIrKh5kpjjHEmjFpEZAowBSApKal5IlVtVllZCmlp08nMfIvKyiwCArpRFnE3szdv4ZNfPqTSUcmY5DE8M/4Zzu55tqslzzH3z6G0xrf5hyb15oEv1wL75jDomxCGj5eNqGBfNmQWAvDZ8rR6k8K9n64mr6SSk3u1dy175dJjXcVPh9I7PoxPbjiOLtHBR/Q5qLbDbUnBGJPm/J0tIp8BQ4EsEYkzxmSISBxQp1mG845iBsDgwYPrJA2lGkNe3lzS019m9+6PARsR7SaxyT6cacu/Yn7KVCL8I5hy7BSuHXQt/dv3r7VvWWVVrYQAMDApnIuGJfHuX7sAmD55oKuSNykykJ/W7WsRVN3ZrLSiisfnbMAmwgdLUgAY1T3Ktd343u1piGM7RjZoe9U2uSUpiEgQYDPGFDofnwL8F/gSuByY6vz9hTviU22T3V5AdvZHpKY+TUnJBry9I4lP+CdzcyN59c+PWJ75OTFBMTxx0hNcM+gaIgLqtvRZm17A16usEtDhnSPx9fbi1hO70i8xnNKKKldSGNtjXye1TlHBLNuV73qeV1JJZJAvU79bz+wFO13LT+kVS4i/Vg6rpuWuO4VY4DPnrbY38K4xZo6ILAY+FJGrgZ3A+W6KT7UhZWU7SUl5hqyst7Hb9xAcPICopKf4Mcvw+BdPkVWcRZ+YPsw+azbn9z4ff2//A77WFa8vZneh1ZHsHyf3YGinfd/Oh3Vux5Pn9SMhIqDWxX1IcgSfLEt1PX9zwQ5uP6l7rYQAcPnxyY30jpU6MLckBWPMNqB/PctzgXHNH5Fqa4wx5OZ+Q3r6y+zZ8w0ivrRrdzp+kVfx0uq5vD73EfLL8hndcTQvn/4yZ/Y485A9f7P2lrkSQoifNz1iQ+ps87fBHeosq25tFBPiR3ZhOc/9tJnbT+peZ7uE8IAjeatKNYinNUlVqkmVlGwiJ+dzMjNfdxYRRdCx4wNk24by5PIPeG/12QBM7D6R+0fdz8D2Aw97GIh3Fu5EBH6+YwzhAT6EBR5eUU91x7VjO0bwnbOHcm6NYSuqtQ878B2KUo1Fk4Jq9YxxkJc3l7S058nN/RowhIYeR48er7O+NJHb/3qeLzc+hI/NhxsG38CNQ26kR1SPBh0jv6SC53/ZQp/4MDpFBTVo33MGJrBgaw4PTurtSgrXv72UQF8vju0YwbzNVv/Oms1QlWoqmhRUq2W3F5CZOZvU1GmUlW3D1zeODh3uJCr2SuamrOXqLx9mReYKYoNi+c+o/3DLsFuICow69Avv5/u1mVz31lIAHKbhDeIignx57XJrDCJfLxsVVQ4W78jD2yb0TQhzJQWlmoMmBdXqFBevJy1tOllZ71FVVUBw8AB69nwTu/8JPLlgGp9+eRKpe1PpFN6J5097nqsHXk2Az+GV11fYHfz9wxVcM6ITA5Os1keLt+/rnDZ98sCjiv3sgQmu5qd2hyHIz5u/7h13RMlGqSOhSUG1ClbF8ZfOiuM5iPgQE3MhCQm3sKlIuGvh87y18nK8bF5M6DaB5097nondJuLj1bAmnluyi/hmVQZz12ex8oFTsIm4Jqt5+ZJBR905rGq/i/+xHSOIDdW6BNV8NCmoFq28PJ3s7A9JTX2a8vJU/PwSSU7+L+3bX8nCzC38/cv7+X7r9/h5+XHbsNu4YcgNdG9Xt2XP4Vq2Kw+AskoHPe6bU2vduEaYwczhqJsUlGpOmhRUi+NwVJKX9yMpKU+Rn/8b4CA09AQ6d55KeOQ5fLLhM6Z+N4HV2atJCEngP6P+wx3H30GoX+hRHbfcXsWr87bVu25458hGGYZ63DGxfLo8DYBTe7fXoa1Vs9OkoFoMu72QtLQXyMycSWnpFnx9E+jY8d/ExFyE+CbxypJXePHDfmzZs4Xk8GRePeNVLuxzIcG+jTPez5IdeezMLWH65IGc2rs96fmlrEor4Pgu7RptGOqJ/eIYkHQim7MKGdMjplFeU6mG0KSgPF5h4VLS018lK2s2DkcZoaHH0bnzVCIjJ7AlbxcPL3idFxa/QFFFESOTRvLkyU8yqcckbNI437LtVQ7e+HMHHy1JxSbWEBW+3jaSo4JIbmDz08OREB6gHdWU22hSUB6poiKbrKx3SU9/mdLSjYh40779FcTFTSEoeBC/7viVh785jd93/o5NbJzV8yxuHnozY5LHNHosny5L45Fv1gNw3rGJOv6QatU0KSiPUly8jtTU58jKehuHo5TQ0BOIj7+e9u0vR7xCeGvlW0xfNIUVmSuIC47jv2P/yzWDrqGyIpSMgjIq7A4cxuDv44Uxhj3FFa7WQUfq3UXWIHbf3TaSnu3rDl2hVGuiSUG5ncNRSU7O56SlTaeg4A9stiCio88lMfEfBAcPoKC8gP8teZ1nFj5H6t5ddIvsxhtnvsF5vc4jyDeIL1akcdv7vwAQ7OdNUbmd6BA/Jg/pwPSft/DTP0bRNebILuYfLN7FipR8bh3XjWPijq6iWqmWQJNCK2GM4cVft5IUGUhJhZ0FW3N5+vwBeHnwLFuFhSvIyHiN3NwvKS9Pwdc3js6dn6B9+8vx9Y1hafpSps+9gk/Xf0pRRRF+VX05u9MzfHLF7bXGI7rt/RWux0XldgB2F5Yzb4vVE/ijJancM+GYBseXUVDKXZ+sBmCwNg1VbYQmhVZi+twtPPvTplrLhnVux+ShnjU7nTFV7N79GenpL5OfPxcRH9q1m0jXrtOIipqEw8D3W7/n0XmPMj9lPuH+4UzqMQn/son8tCqUZRuFcrvDNQ7Q6tQCwBphtFd8KFt3F3H2gASm/7zF1eb/gyUpZO0to3N0MMd1aUeIvzdBvt50OMisZRkFpRz32M8ATBnVmZHdGj78hVItkSaFVmLa3E11lt3z6WrOHpjgEQOplZdnkpX1Jqmpz1JRkYm/fyc6dXqUuLhr8PWNpspRxczlViuiFZkriAmK4amTn+KqgVcRERDBOS/OR8gH4KOlqYzvFcuE6fPIKaogLsyf96cMp0NEICLw/VprFrNs5zDW+SWVfL4i3Qrkx30x3TfxGBZu28OJPWM4qVcMMSFWz+HMgjJXQgj19+ae03oe9kipSrV0mhRaiRB/HwpKK5k8NImkyEAen2NNeZ1TVE5ixOHN49vYjDEUFa0kJeUpcnI+x+EoJixsNF27Pk909NmIeLE9bzsfL36DpxY8RXZxNv1i+zH7rNlc0PsC/Lz3VRAv25XP0E6RLNq+h/s/X8P9n68BoHN0EO9fO5yYGkNBRDiHrM4oKDtofNUtin5an8XPG2J57fLBlNuruObNxQBcMjyJW07spglBtSmaFFqBgtJKSiurGNopksfO6QtA15hgrn1zCblFFc2eFIypcjYnfYW9e+fj5RVMbOxFJCb+A/+AHvzzoxXg+zlby97kuy3fYnfYGd1xDDNOn8GkHpNqXYTnrs/iB+c3//gwf/x9bJRVOlzr59w2Cl/v2v0RBiZFEBXsS05RBR3bBbIzt8SVUO6beAxXntCJF3/Zwmcr0rh+dBfu/HgVP63PIvnubwgLsJLrtAsHcOaAhGb5vJTyJJoUWjhjDP0f+gGAi4ftqz/oHmv14l20fQ/hgT488s16njm/f5O2sd+7dxG7d39CZuZsKiuz8PfvRNeuzxETcxGrM7zZlg8L1r7PS2sfodxrHd6E0j3kfPJ3j2H7hjge2OXLkn5raR/mT1G5nYuHJXH17CWu1z+9Xzx3nNKDez9bzaLte7hkeMc6CQHA19vGiT1j+HBJKuN6xnLPhJ6AVZxU3SnslnHduGVcNwC6RAdz7kt/AvsmvDm+i9YhqLap2ZOCiHQA3sSap9kAM4wx00TkQeBaYLdz03uNMd82d3wtzdr0va7Hg5P3zQfcsV0Q/RPD+L9v1/Pod+sxxmqFc9WITo16/KqqUnJzvyY19Vn27l0A2IiMPI34+Gtp18761l9mL+OUGXdR6P05lbZdeNkiiKiYQlDVWIpLQ6hOU/kllby1cN+8xC/9urXWsbrFBtMhMpC3rh52yLhuO6k7m7KKuOy4jq7xgw7US/jYjhGs/++pvLdoF5VVDry9bESHHF3fBqVaKnfcKdiBO4wxy0QkBFgqItXVf88aY55yQ0wt1i8bsgG469SedS56U0Z14aZ3l1E9GvPO3OJGO25Z2U4yMmaRkfEqFRUZBAR0p3Pnx4mPvw5v7zAAckpymLV8Fk/Mf4I9vrn4OroyMeERVm/pyxXHdcZmE3KLKnhwUm/mrMnk3s9W13usm8Z2YWCHCDq2O/whJRLCA/j8phMOe/sAX69GT5hKtUTNnhSMMRlAhvNxoYisB7Tw9gi889dOnv5xEz1iQ7hhTJc66yf0bV/r+ewFO7l4eEe61zOh/OFwOCrJzv6A9PQXXXcF4eFj6NFjJhERJ2GzWd/5d+Wn8vj8qby75h3yy/I5tv0IvPJPxt8xkDVbbJx8TCwPTupdq+7gomFJTBoQT0Z+Kb9t2o2ft43KKoMBrjohWSt7lWombq1TEJFkYCDwF3ACcLOIXAYswbqbyKtnnynAFICkJM9qg9+cdheW8+/PrBY4fxucWO82IsIdJ3fnmZ82ue4WHv9uAzOvGNKgY+3du4ScnE/JzHyTioo0/Pw60Lnzk0RFncldXxQh6+Gxc+DrzR/y9B+zWJz5Azbx4oI+f+PuEXeTnRvLNduXMDQ5kkU7rMre+i7ywX7edIsNodsRJi2l1NET46Zp/kQkGPgN+D9jzKciEgvkYNUzPAzEGWOuOthrDB482CxZsuRgm7Ra7/y1k39/toYPpgxnWOd2B93WXuWg67+/A2BIcgQfXX98vdvNXZ/F1bOXsOCeE2kXsJfMzDfIzHyDkhKreWtk5ATi46+nXbuJiNjILChj6GNfU+w1jzL/TylxpOJlIgiyjyG46lSSw7oyvnd7Zs3fDsDPd4wmKsSPUB1QTim3EpGlxpjB9a1zy52CiPgAnwDvGGM+BTDGZNVY/yrwtTtiayl25Zbg621jSI3K5QPx9rLx1c0juOjVhZRUVB1wu2d/WEfPyFVs2vghlL6PMRWEh48hPv5GYmIuwNd33/j+WUVZ3PPTM6T5z8Ah+fjau9HO/g9uGnoFZ/RPYNrczczbnONKCDaB+PAAj+hIp5Q6MHe0PhJgJrDeGPNMjeVxzvoGgLOBNc0dW0uSmldKYngAtsMc26hvYhjj+7TnT+d4QFe9sZi8kgqGdWrHuf0N9uJPubrHM0T478FeHEBC3MUkJt5OcHA/12sYY/h5+888veBpvtvyHRjB39GPfx3/MiHSjwEdIhnXMwabTXjr6mGc9cJ8VqcV8K/xPbh2ZGePHodJKWVxx53CCcClwGoRWeFcdi8wWUQGYBUf7QCuc0NsLUK5vYrN2YUkHmTsnvpEBvmyp6SClSn5/LYxnQExiwgv/ZK0TVb+3V3ai3fWT2FVzmD+fvIAru/RGYC95Xv5YsMX3DXnKTLKVuFFEGGVFxJYNQpfk8QlA0fVW3n91tVDyS2qaJKJaJRSTcMdrY/+AOr7yqh9Eg5gY2YhBaWVrEjJ46Vft5JXYnWwumR4xwa9TkSgL17k8+p3t/HYyB+ICcykoDycjzZdxsb8k4iJ6EZIuI2KrN08PmcDz//xDYOOWcKnGz6m1F6KtyORCPt1BFedgo197fiD/Oo/jUL8fXRCGqVaGO3R7OG27i5i/HO/11n+t2MTGzQC6t69S+jo/QzTxn6It62KnYUD+d/yK1mWPRyHscr5n57ck225hfy+60dSHW9SUbWJHRtCmdjtbOat6IOfozfje8Xj42UjNMCHb1als7fM3mjzEyul3E+TggcwxhywHX515zSApMhA/jm+B2N7RBPs533ItvtWb+NvSEl5isLCvwjAn9/STuKXlNO4/6wLeWxoIGWVDp7+cSODOzt4a/0jvLP6HTLJpH1IAuV51xBefiqLl/lTPdzcjMv2NVj4v7P6kFtcQfAB7hSUUi2P/je7kTGGN/7cwRt/7uDNq4bSsV0QpRVVfLgkhb+25+JwwJy1mQAsv/9kIoJ8D+t1KytzSU2dRmbmG5SXp+Dv35nOnadS5X8ZV85ZBkCP9iEkRgTw1aavyPZ9mVt/nYOIcFbPs7ioz0Wc3v10bn53NT+uyzrgcWw20eEglGplNCm4yYKtuby/eBdfOMf5H/3kr/z+r7G8Om9brfF/qh1OQigomE96+stkZb0HGMLDx9C9+yu1ehs/e0F/NmTm8nvqZzz6/qOs272OuOA47ht1H5f3v5wukft6Rk8Z1ZnNWYVcfnwyyVFBRB/lXMdKKc+nScENduYWM/nVhQDEhfmT3C6IBdtyGfWkNc9w/8QwTu4Vy8XDOvLHlpyDNuUsL08nN/drMjJmUVj4FzabPwkJNxMXdw3BwX1qbVtYXsim4nd4Yf3zpC1Ko19sP2acPoMrB16Jt63uqTAkOZJf/zW2Ed+5UsrTaVKowRjDT+uzGdU9Cj/vxu9kZYxhY1Yhpz43D4DkdoHMvWMMNoEpby3lx3VZjO4ezSNn9XFNFXlG//h6X6eoaBmpqc+Rnf0hxlQQGNiLLl2eIT5+Cl5etZuAphSkMO2vacxcPpP8snxO6HACMyfNZFzncfUmA6VU26VXBKCssor3Fu3ioa/WAdbgbI+e3de13hhDWaWDAN8jSxTGGN5euJOvVmawaMceAF64aBAT+8W5tnn1snp7nNdSVVXG7t0fkpo6jaKiZXh7h9O+/ZUkJNxAUFBfRGrPLbAycyXPL3qe11e8jsM4mNxnMrcNu41hiYceelop1Ta1zaSwfTs7r72Vv7LLKPcLwMvfn8IqGzf4+lPq7Yd9jT9pmf35YG0OReLD5sIqKv0CKPP24ewR3Tnr+G6ERYVDYCAcogXQwm253P/5GjZnFxEb6scZ/eMZ3zu2VkI4lLKyVNLTXyQzczYVFenOyWueJzb2Ynx8Impt6zAO5u+az8O/P8zc7XPx9/bnumOv4+/D/063dt2O5NNSSrUhbTIplOXmYV++ghGVZQRWluFbVUlgZXntjb6Bf9S384v7Pff3Bz8/CAqyfgICsAcEsq3EkFoGxV6+XOPjT/dOMQzoEY+kRsPkfx1WnPn5v5Oe/jLZ2e8DhnbtziAhYRYREafUaY7qMA7eW/0e0xdNZ1HaIqIDo7lv5H3cPvx2IgIi6j+AUkrtp00mhZWRHbn4uld49fLBjOoWjaset7QUU1zMh79vZNO2LP7WK5Job4NfZQW2shKK8/ayfmsWaWk57EjNIbCinFgfByOSQqjI30tmZh5VRcVQUEJgZRnt7eW0s1URJZV4pZTC96UQEQH/OnBSsNuLyMn5jF27HqekZC3e3hEkJt5OfPx1BAb2qLP99rztfLzuY15e+jLb8raRHJ7MK6e/woV9LiTUL7SJPkGlVGvltqGzG8PRDJ2dV1xBaIDPEQ/SllNUzi3vLmfBttwDbrPmofEE+XrV/lZvt4N37VxsjIO9exeSkvIUe/Z8h8NRRmBgbxISbqB9+6vw8qo7jeSa7DU8Mf8J3lvzHnaHneM7HM8tQ2/hgt4X6IQ0SqmD8rihsz3B4XYEO5CoYD/eunooP67L4qf1Vq/jsT2jOa1PHGl5pRRX2Ovv6VsjITgcFa4pLa2K4wji4qYQHX0eYWEn1Kk4dhgHc7fNZer8qfy8/WfC/MK4dtC13HHcHXSO6KzJQCl11NpsUmgM3l42Tusbx2l9a1caJ7U7+OilJSWbycycRXr6y9jt+QQG9qJ791eJifmba37jmhzGwbur32X6X9NZnL6YyIBIHj3xUa4ZdA3RQdGN+p6UUm2bJoVmYrcXkpPzKWlpL1BYuAQwREefR1zcFCIjT653n7zSPN5d/S6P/vEo6YXpHBN1DDNOn8El/S4hwKdukZJSSh0tTQpNrKwslbS06WRkzMRu30NQUB+Skx8gLu4a/PwS6t0ntySXJ/98kpnLZ5JTksNxicfx3PjnOLfXudj2K1JSSqnGpEmhCRhjyMv7kbS0F8jN/RoRLyIjx5OYeAfh4SMRqdsJzhjDN5u/4Z3V7/D5hs+prKrk1K6n8p/R/2FI/BCtL1BKNQtNCo3Ibi8iK+tN0tNfobh4FV5eoSQl3U1c3DUEBHSqd5+Kqgo+WvsRTy94muWZy4kMiOSqAVdxw5Ab6BPTp959lFKqqWhSaAQlJRtJT3+V9PSXcDhKCAkZTI8erxETc1G9zUkB8svyeX356zzx5xNkFmXSN6Yvr5z+ClcOuBIfL520RinlHh6XFETkVGAa4AW8ZoyZ6uaQ6mW3F5Cd/T4ZGa9RWLgUES+ios4mIeEmwsJG1Vvc4zAOVmetZvbK2by58k1yS3M5LvE4Zpw+gwndJuBla/xB+JRSqiE8KimIVdj+AnAykAosFpEvjTHr3BvZPqWl20lJeZrs7Pex23MJDOxFcvIDxMdfj69v7EH3fWnxS9z83c3YxMY5x5zDncffyZCEIc0UuVJKHZpHJQVgKLDFGLMNQETeB84E3JoUjDHOOQtmOCuOfYiKOpvExL8TGjrssCuBJ3afSIhfCOM6jSMhtP6WR0op5U6elhQSgJQaz1OBWuM8i8gUYApAUtLhT1x/JIqLN5CT8ykZGbMoK9uKj08UyckP0r79Ffj7d2zw6yWHJ5Mcntz4gSqlVCPxtKRwSMaYGcAMsMY+auzXdzjs5Of/Smrq0+zZ8wPgIDT0BDp2vI/Y2Euw6aQ0SqlWzNOucGlAhxrPE53LmpzdXkRGxgzS01+mtHQzvr7xJCXdSULCLfj51Z39TCmlWiNPSwqLgW4i0gkrGVwIXNRUBzPGwZ49c9i9+1N27/6AqqoigoMHccwx7xIVdSZeXgcfw0gppVobj0oKxhi7iNwMfI/VJHWWMWZtYx/H4bCTkfEKaWn/o6RkAyJ+xMZOJj7+ekJDdapKpVTb5VFJAcAY8y3wbVMeo6BgHps330xo6PH07PkGMTEXYrP5NeUhlVKqRfC4pNAcIiLGMmDAPOecBTqmkFJKVWuTSQEgPHyEu0NQSimPo+MwK6WUctGkoJRSykWTglJKKRdNCkoppVw0KSillHLRpKCUUspFjGn0MeWajYjsBnYe4e5RQE4jhtNYNK6G8dS4wHNj07gapjXG1dEYE13fihadFI6GiCwxxgx2dxz707gaxlPjAs+NTeNqmLYWlxYfKaWUctGkoJRSyqUtJ4UZ7g7gADSuhvHUuMBzY9O4GqZNxdVm6xSUUkrV1ZbvFJRSSu1Hk4JSSikXTQpKKaVcWn1SEBGPe48iMklEurg7jpZCRC4Skf7Oxx41K5KeXy2fJ59f7uBxJ3RjcP5T/MPdcexPRE4SkQXATCDO3fFUE5GzRORhd8exP+fnNQ94DhgIYDygZYSeXw3nieeYp55f4N7Pq1XNvCYi3sAdwA1Akoj8bIxZISJexpgqN8UkQBDwHhAC3AfcDnQE/hARmzHG4aa4bMCVwN1ARxH5wRgzr7ljqScuf2A2EAM8ApwJBDrXu/NvqedXw2PzqHPMw88vj/i8WtWdgjHGDmwEegL/AF5xLnfLH9l5bGOMKQLeNsaMMcbMBb7HOhFx1z+sM64qYAvWt6QbAbd/k3PGVQq84/y8vgf+BC51rnfn31LPr4bH5lHnmIefXx7xebX4pCAit4rIVBE537noG2NMmTHmOSBGRC5ybufjprj+BmCM+cC53AbkASki4tecMdWI61URuca56DdjTKEx5lUgSESurhGnO+K6FsAY84VzuRewHVgrIh2aM6Yacen51fDYPOoc89Tza7/YPOPzMsa0yB9AgL8D84HzgPXAFUBMjW3OBtI8JK7oGtscD2xww2d2BbAQOBX4DbgH6FJj/WnAWiDCzXHdC3Susb4vsBgI8YC/o55fLewc88Tzy5M/rxZ7p2CsT2wscJ8x5mOsf5R+wPga23wGbBKRf4JVseSmuPpj/dGrt/kTSBWRSU0dz37GAY8bY+ZglY37AxfXiOs7rIvMFBEJqf4W6oa4fIFLasS1GigDLmymePT8OnKeeI553Pl1kNjc/nm1iKSwfzOxGrdRS4CRAM4PdTPQW0R61Nj8BuAJEckEEtwU1yZnXD2d24UCG4DKxoznIHFWx7UcON0Z1xJgAZAgIifU2Pwu4DGsz7K9m+Ja6IxrhHM7wSon92+OJoOecn41IC63nl/7xeYx55innl+HiM2t/5PQQpICEFDzidlXebYFCBGRvs7nvwFhWK0wEJEBwKvAJ8AgY8xsN8cV7NxuL5AIxDZyPICrnNSVtGrENR+wicgo5/M1QAYQ79y+K/Ai8DnW5/W8G+NKx9ms0vntOAYodj5uVAeJy63n1xHE1SznV434XNcPDzrHDjemZju/nHHVSjae8nnVx6OTgogMF5FPgBdE5JQa/yTVTWkXAXbgFBHxNsasw/q2Vj3xRC5wozHmb8aYdA+KC+BCY8wbjRWT8/jHicirwN9FJKT6BK8R12as8skLxGp6l4p14Uh2ri8AbjbGnNPIn9eRxNW+RlwA/zTGzGqsmJzHP0FEZgP3iUhkjbiqK43ddX4dbVzQBOeXM4ahInIr1G7ZVONi3Ozn2BHG1OTnV43YXgXuEpHoGsu9DhJbk/9PHozHJgURGYOVIT/FagZ4CRAhVrtrO4AxZgvWrXQXrHa9AOU4p+g0xqQ4yws9Ja4d1a9jjClr5LhGA/8Dfsb6lnGviJziPJbduVkhMA/wA55yXmQisC5uGGN2G2M2e1pczm0rGjmuzlh/x1+w2vQ/LCITnMeqdP52x/l1NHHtqH6dxj6/nLHdDnyGlaxOcy7zch6v+mLcrOdYY8Tk3Laxzy8vEXkMa3jr+cAg4AERiXUer7rpa7P/Tx6KxyYFrEq9xcaYd4C3AR+gqPoPLSKPiMhMYCkwHRgqIkuBPVjlg54Y1w9NGNexwHxjzHtYHXJigcnVJ6GIPAK8i/XN436sE2+e83ljF6u1hLiGAuud36b/CawAzhCRuOq43HR+HU1cTXl+gdV083SsepS7oXa7fhF5iOb/W3piTNXSgPOdf8u/A8OpUeTs5tgOzLih2Vp9P1gfWPcazwdgnegPAFnAr8As4AKsJnfvAl1rbB8MhLfhuCYCbwLxzufTgXeA64DuzrhqNnWz0QRN8Dw4rjOAm4Hhzuedsb7BJTmf9wKmYv3zjmjGv6NHxnWA2LycP/7At8CtNf5mfZvjb+mJMdUT2xDn80jnbz/n78+Bwc7H/Zoztga9D7cHAOHAN1i3UfcBwTXWDcW64J7rfH41VsVe/5ofpMZlALphFdP8gFXx+RnwL6yyUtpwXHHAV1jfwO7Hat433rnuKeAO52MvrF6tDwBhbTWuw4itemKuccBKIKqe/Rs9Nk+M6RCxnbLfNiHO2OKbM7Yj+fGE4qMgrNvxW5yPR1avMMYsAqJxluFilUuHY/XYRJp2XJeWEtcoZ0ybsYZeeAz4yBhzNlYF1pjqHdtoXIOBecaYkcaYh4FpwBTnunlAXxEZZqwihzRglDGmoA3HVV9szwHXQ60B437Batp5izOmoc7f0kSxeWJMB4vtxv22GQqsNcaki0iwiHRrptgazC1JQUQuE5HRIhJqjEnDqoz5EKsDyTARqW6O5Yc1Lkn1BzwOiHRuR2N/mC00rqHVcRljKowxvxhj3nfuOgiYU/06bSyuMc6/01zgrRqrc7Ha9QP8hdVO/BkRCQZ6AztFJLAtxXUYse3B+vbratHjjOERrFY1BcAg5wWu0Zp0emJMDYhtnXO76hZjEVhDj1yJ1Xt6gDPmJmkCezSac+wREZE4EfkFuByr195LIhJlrLFkSoCfsD68cQDGmHLgSyBYRH4HJmM1z8rWuGrFdeJ++45wVj6OBL5urJhaWFwXYRXxBRpjMmr8c8Y5Y8MYk2mMmYZ1EZ6F1ZLsced7aNVxHUVsDud+XbHKxOcDI4wxLzfGBc4TYzrK2Ko7EJ6JVWw6CrjAGPNRY8XV6JqjjArwcv7ujjWaI1hlpc8Dn+637d+xsn04EOBcFkCNsUo0rnrjCgOCnMvigQka1764amzzFXCS83GM87c3TVO57ZFxHWVs1ZWnMcDY1h5TI8QW5fw9GTivKWJr7J8mnU9BrPbCDwNeIvItEApUgdVsTERuA9JFZLQx5jfnbq9iXUx+xBqzfpCxiia2aVyHjKujiBxrrA4wjdmZqlXEJSK+wG6s8Yr+DzhdRMYYY/KwKshbdVyNGNtYY90VN8qdsSfG1MixjTJWk+wWocmKj8TqtLQU6zZqC9YHWwmMFWcFkLHKAB90/lSbiFVWvwLo67zwalyHjmulM65UjatOXA85d/PHGpVyLlZrkJOcF95WH1cjx7anNcfUBLEVNHZsTaqpbkGwyo0vrfH8RawOJlcAS53LbFjdzT8Ekp3LzsRqaaFxaVyNGVciVguQN4EBbS0uT43NE2NqCbE16ftuwg80EKvrdnU528XAY87HK4BbnI8HA+812xvWuNpiXO+39bg8NTZPjKklxNaUP01WfGSMKTHGlJt9Xc5PxiprA2sO0mNE5GusuWWXQd2RBDUujauR4lra1uPy1Ng8MaaWEFtTatKKZnBV1BisMW++dC4uxJr9qA+w3TjL540z7TYHjUvjaotxeWpsnhhTS4itKTRHPwUH1qBxOUA/Z2a9H3AYY/4wjVxhq3FpXBpXi4zNE2NqCbE1vuYoo8IaJM0B/AFc3RzH1Lg0Lnf/eGpcnhqbJ8bUEmJr7J/qgaSalIgkYg3q9YyxegN7BI2rYTSuhvHUuMAzY/PEmKp5cmyNrVmSglJKqZbBE0ZJVUop5SE0KSillHLRpKCUUspFk4JSSikXTQpKKaVcNCko1QAiUiUiK0RkrYisFJE7xDnz10H2SRaRi5orRqWOhiYFpRqm1BgzwBjTG2ssnNOABw6xTzLWLF1KeTztp6BUA4hIkTEmuMbzzlhz7kYBHbHm6g1yrr7ZGPOniCwEjgG2A7OB6cBUYAzWKJwvGGNeabY3odRBaFJQqgH2TwrOZflAD6xB0hzGmDIR6YY1lPhgERkD/NMYc7pz+ylYU24+ItbE7/OBvxljtjfjW1GqXk0+SqpSbYgP8D8RGYA1ZWP3A2x3CtbAauc5n4cB3bDuJJRyK00KSh0FZ/FRFdbcwA8AWUB/rPq6sgPthjVBy/fNEqRSDaAVzUodIRGJBl4G/mesctgwIMNY8/ZeCng5Ny3Emq+32vfADSLi43yd7iIShFIeQO8UlGqYABFZgVVUZMeqWH7Gue5F4BMRuQyYAxQ7l68CqkRkJfAGMA2rRdIy50xdu4Gzmid8pQ5OK5qVUkq5aPGRUkopF00KSimlXDQpKKWUctGkoJRSykWTglJKKRdNCkoppVw0KSillHL5f9u8nbvcDvpDAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.387Z",
          "iopub.execute_input": "2022-04-14T00:27:12.392Z",
          "shell.execute_reply": "2022-04-14T00:27:12.546Z",
          "iopub.status.idle": "2022-04-14T00:27:12.516Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b1 = yf.download(market1, start=start, end=end)['Adj Close']\n",
        "b2 = yf.download(market2, start=start, end=end)['Adj Close']"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[*********************100%***********************]  1 of 1 completed\n",
            "[*********************100%***********************]  1 of 1 completed\n"
          ]
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.525Z",
          "iopub.execute_input": "2022-04-14T00:27:12.532Z",
          "iopub.status.idle": "2022-04-14T00:27:12.961Z",
          "shell.execute_reply": "2022-04-14T00:27:12.986Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mlr = regression.linear_model.OLS(asset1, sm.add_constant(np.column_stack((b1, b2)))).fit()\n",
        "prediction = mlr.params[0] + mlr.params[1]*b1 + mlr.params[2]*b2\n",
        "print('Constant:', mlr.params[0], 'MLR beta to S&P 500:', mlr.params[1], ' MLR beta to MDY', mlr.params[2])\n",
        "\n",
        "# Plot the asset pricing data and the regression model prediction, just for fun\n",
        "asset1.plot()\n",
        "prediction.plot()\n",
        "plt.title(symbol1 + ' ')\n",
        "plt.ylabel('Price')\n",
        "plt.legend(['Asset', 'Linear Regression Prediction'])"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Constant: -58.32215050221849 MLR beta to S&P 500: -0.08513423266658202  MLR beta to MDY 0.013905040520174692\n"
          ]
        },
        {
          "output_type": "execute_result",
          "execution_count": 12,
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x18e7bbd0978>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:12.970Z",
          "iopub.execute_input": "2022-04-14T00:27:12.977Z",
          "shell.execute_reply": "2022-04-14T00:27:13.232Z",
          "iopub.status.idle": "2022-04-14T00:27:13.135Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Compute Pearson correlation coefficient\n",
        "sp.stats.pearsonr(b1,b2)[0] # Second return value is p-value"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 13,
          "data": {
            "text/plain": "0.9868492914594209"
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:13.143Z",
          "iopub.execute_input": "2022-04-14T00:27:13.148Z",
          "iopub.status.idle": "2022-04-14T00:27:13.160Z",
          "shell.execute_reply": "2022-04-14T00:27:13.237Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Multiple Linear Regression"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "slr = regression.linear_model.OLS(asset1, sm.add_constant(asset2)).fit()\n",
        "print('SLR beta of stock2:', slr.params[1])"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "SLR beta of stock2: 2.6569820300692166\n"
          ]
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:13.168Z",
          "iopub.execute_input": "2022-04-14T00:27:13.174Z",
          "iopub.status.idle": "2022-04-14T00:27:13.186Z",
          "shell.execute_reply": "2022-04-14T00:27:13.242Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Run multiple linear regression using asset2 and SPY as independent variables\n",
        "mlr = regression.linear_model.OLS(asset1, sm.add_constant(np.column_stack((asset2, benchmark)))).fit()\n",
        "\n",
        "prediction = mlr.params[0] + mlr.params[1]*asset2 + mlr.params[2]*benchmark\n",
        "prediction.name = 'Prediction'\n",
        "\n",
        "print('MLR beta of asset2:', mlr.params[1], '\\nMLR beta of S&P 500:', mlr.params[2])"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MLR beta of asset2: -0.23646687078090445 \n",
            "MLR beta of S&P 500: 0.5092140705462285\n"
          ]
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:13.194Z",
          "iopub.execute_input": "2022-04-14T00:27:13.200Z",
          "iopub.status.idle": "2022-04-14T00:27:13.212Z",
          "shell.execute_reply": "2022-04-14T00:27:13.246Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the three variables along with the prediction given by the MLR\n",
        "asset1.plot(label=symbol1)\n",
        "asset2.plot(label=symbol2)\n",
        "benchmark.plot(label=market1)\n",
        "prediction.plot(color='r', label='Prediction')\n",
        "plt.title(symbol1 + ' & ' + symbol2 + ' Price')\n",
        "plt.xlabel('Price')\n",
        "plt.legend(bbox_to_anchor=(1,1), loc=2)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x18e7cc72160>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:13.220Z",
          "iopub.execute_input": "2022-04-14T00:27:13.226Z",
          "shell.execute_reply": "2022-04-14T00:27:13.387Z",
          "iopub.status.idle": "2022-04-14T00:27:13.364Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot only the dependent variable and the prediction to get a closer look\n",
        "asset1.plot(label = symbol1)\n",
        "prediction.plot(color='y')\n",
        "plt.xlabel('Price')\n",
        "plt.title(symbol1 + ' Price')\n",
        "plt.legend()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 17,
          "data": {
            "text/plain": "<matplotlib.legend.Legend at 0x18e7cd05da0>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2022-04-14T00:27:13.375Z",
          "iopub.execute_input": "2022-04-14T00:27:13.381Z",
          "iopub.status.idle": "2022-04-14T00:27:13.531Z",
          "shell.execute_reply": "2022-04-14T00:27:13.544Z"
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mlr.summary()"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 18,
          "data": {
            "text/plain": "<class 'statsmodels.iolib.summary.Summary'>\n\"\"\"\n                            OLS Regression Results                            \n==============================================================================\nDep. Variable:              Adj Close   R-squared:                       0.881\nModel:                            OLS   Adj. R-squared:                  0.881\nMethod:                 Least Squares   F-statistic:                     3735.\nDate:                Wed, 13 Apr 2022   Prob (F-statistic):               0.00\nTime:                        17:27:18   Log-Likelihood:                -3969.0\nNo. Observations:                1008   AIC:                             7944.\nDf Residuals:                    1005   BIC:                             7959.\nDf Model:                           2                                         \nCovariance Type:            nonrobust                                         \n==============================================================================\n                 coef    std err          t      P>|t|      [0.025      0.975]\n------------------------------------------------------------------------------\nconst        -96.3183      3.345    -28.796      0.000    -102.882     -89.755\nx1            -0.2365      0.076     -3.097      0.002      -0.386      -0.087\nx2             0.5092      0.007     76.601      0.000       0.496       0.522\n==============================================================================\nOmnibus:                       62.225   Durbin-Watson:                   0.023\nProb(Omnibus):                  0.000   Jarque-Bera (JB):               72.473\nSkew:                           0.650   Prob(JB):                     1.83e-16\nKurtosis:                       2.814   Cond. No.                     2.81e+03\n==============================================================================\n\nNotes:\n[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n[2] The condition number is large, 2.81e+03. This might indicate that there are\nstrong multicollinearity or other numerical problems.\n\"\"\"",
            "text/html": "<table class=\"simpletable\">\n<caption>OLS Regression Results</caption>\n<tr>\n  <th>Dep. Variable:</th>        <td>Adj Close</td>    <th>  R-squared:         </th> <td>   0.881</td>\n</tr>\n<tr>\n  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.881</td>\n</tr>\n<tr>\n  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3735.</td>\n</tr>\n<tr>\n  <th>Date:</th>             <td>Wed, 13 Apr 2022</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n</tr>\n<tr>\n  <th>Time:</th>                 <td>17:27:18</td>     <th>  Log-Likelihood:    </th> <td> -3969.0</td>\n</tr>\n<tr>\n  <th>No. Observations:</th>      <td>  1008</td>      <th>  AIC:               </th> <td>   7944.</td>\n</tr>\n<tr>\n  <th>Df Residuals:</th>          <td>  1005</td>      <th>  BIC:               </th> <td>   7959.</td>\n</tr>\n<tr>\n  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n</tr>\n<tr>\n  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n</tr>\n<tr>\n  <th>const</th> <td>  -96.3183</td> <td>    3.345</td> <td>  -28.796</td> <td> 0.000</td> <td> -102.882</td> <td>  -89.755</td>\n</tr>\n<tr>\n  <th>x1</th>    <td>   -0.2365</td> <td>    0.076</td> <td>   -3.097</td> <td> 0.002</td> <td>   -0.386</td> <td>   -0.087</td>\n</tr>\n<tr>\n  <th>x2</th>    <td>    0.5092</td> <td>    0.007</td> <td>   76.601</td> <td> 0.000</td> <td>    0.496</td> <td>    0.522</td>\n</tr>\n</table>\n<table class=\"simpletable\">\n<tr>\n  <th>Omnibus:</th>       <td>62.225</td> <th>  Durbin-Watson:     </th> <td>   0.023</td>\n</tr>\n<tr>\n  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  72.473</td>\n</tr>\n<tr>\n  <th>Skew:</th>          <td> 0.650</td> <th>  Prob(JB):          </th> <td>1.83e-16</td>\n</tr>\n<tr>\n  <th>Kurtosis:</th>      <td> 2.814</td> <th>  Cond. No.          </th> <td>2.81e+03</td>\n</tr>\n</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.81e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
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